Robot-Robot-Human Interaction is an emerging field, holding the potential to reveal social effects involved in human interaction with more than one robot. We tested if an interaction between one participant and two non-humanoid robots can lead to negative feelings related to ostracism, and if it can impact fundamental psychological needs including control, belonging, meaningful existence, and self-esteem. We implemented a physical ball-tossing activity based on the Cyberball paradigm. The robots’ ball-tossing ratio towards the participant was manipulated in three conditions: Exclusion (10%), Inclusion (33%), and Over-inclusion (75%). Objective and subjective measures indicated that the Exclusion condition led to an ostracism experience which involved feeling “rejected”, “ignored”, and “meaningless”, with an impact on various needs including control, belonging, and meaningful existence. We conclude that interaction with more than one robot can form a powerful social context with the potential to impact psychological needs, even when the robots have no humanoid features.